Online Resource Allocation in Episodic Markov Decision Processes
It addresses resource allocation in dynamic environments for applications like inventory management, but is incremental as it improves upon existing regimes.
This paper tackles the problem of online resource allocation in episodic Markov decision processes with unknown non-stationary dynamics, proposing an algorithm that achieves near-optimal regret bounds of $ ilde O(ρ^{-1}{H^{3/2}}S\sqrt{AT})$ for both observe-then-decide and decide-then-observe regimes.
This paper studies a long-term resource allocation problem over multiple periods where each period requires a multi-stage decision-making process. We formulate the problem as an online allocation problem in an episodic finite-horizon constrained Markov decision process with an unknown non-stationary transition function and stochastic non-stationary reward and resource consumption functions. We propose the observe-then-decide regime and improve the existing decide-then-observe regime, while the two settings differ in how the observations and feedback about the reward and resource consumption functions are given to the decision-maker. We develop an online dual mirror descent algorithm that achieves near-optimal regret bounds for both settings. For the observe-then-decide regime, we prove that the expected regret against the dynamic clairvoyant optimal policy is bounded by $\tilde O(ρ^{-1}{H^{3/2}}S\sqrt{AT})$ where $ρ\in(0,1)$ is the budget parameter, $H$ is the length of the horizon, $S$ and $A$ are the numbers of states and actions, and $T$ is the number of episodes. For the decide-then-observe regime, we show that the regret against the static optimal policy that has access to the mean reward and mean resource consumption functions is bounded by $\tilde O(ρ^{-1}{H^{3/2}}S\sqrt{AT})$ with high probability. We test the numerical efficiency of our method for a variant of the resource-constrained inventory management problem.